In ordinary holography, coherent light emanating from a source region is caused to interfere with a coherent reference beam in order to construct an interferogram in which the three-dimensional characteristics of the source region are encoded. Conoscopy is a distinct interferometric technique capable of determining the distance to a point within an object volume without employing a reference beam. Instead, light emanating from a source region is prepared in a defined state of polarization and then passed through an anisotropic optical element in which one polarization suffers phase retardation with respect to the other. The two polarization components emerging from the anisotropic optical element interfere with one another, producing a interferogram in the detector plane. The interferogram can be recorded using various means, the most useful being an electronic detector array such as a charge-coupled device (CCD) camera. The electronic image of the interferogram may then be deconvolved to determine the three-dimensional locus of the origin of the light. Conoscopy, thus, requires only a single camera for determining object contour. Furthermore, the source of illumination is not required to be coherent.
Conoscopy is the subject of various patents, including U.S. Pat. Nos. 4,602,844, 4,976,504, 5,081,540, and 5,081,541. Several embodiments have been taught which differ in the method of illuminating the object volume. The light which emanates from the source region may be actively provided, such as by a scanned beam, in which case additional information regarding the position of illumination at a particular time is available for deriving from the conoscopic interferogram the precise three-dimensional profile of the source region. Alternatively, a passive technique exists, referred to in the art as "conoscopic holography," in which diffuse light is used. In the latter case, no additional information is available and the deconvolution of the conoscopic image is significantly more computationally complex. The source region may be illuminated with a narrow beam, providing the conoscopic interferometer with, essentially, a point source in the object volume. A system employing this mode of operation is referred to as a conoscopic "probe." Alternatively, the source region may be illuminated with a grid (or "cloud") of points, or with a line. A system employing a line of illumination is referred to as a conoscopic "profilometer."
Common to the modes in which conoscopy is employed is a uniaxial crystal, which exhibits different indices of refraction (and, as such, is birefringent) for components of light polarized in directions parallel or normal to a particular axis referred to as the crystal's extraordinary axis. The prior conoscopic art may be understood by reference to FIG. 1. As shown in FIG. 1, light emanating from a point P in the object region is circularly polarized by polarizer 16, introducing a 90.degree. phase shift between the two polarization components. The phase components are differentially delayed in uniaxial crystal 14, and then analyzed by means of polarization analyzer 18, which is circular polarizer. Other embodiments are known in the art in which one or both of the polarizer 16 and the polarization analyzer 18 is replaced by a linear polarizer. These embodiments are described in U.S. Pat. Nos. 4,602,844 and 4,976,504, which are incorporated herein by reference. The overlay of polarization components gives rise to the cylindrically symmetric pattern known as a Gabor Zone Lens (GZL) , shown in FIG. 2. The projection of the cylindrical interference pattern on detector plane 14 has, essentially, a quadratic dependence on distance from the center of the GZL, for reasons discussed in detail by G. Sirat, Conoscopic Holography: Part I, Basic Principles and Physical Basis, Journal of the Optical Society of America A, 9:84 (1992), which is hereby incorporated by reference.
Sirat teaches that the response of the recording means in the detector plane is proportional to the modulus of the impinging light intensity, where the light amplitudes are expressed as complex values. In the language of quantum optics, the recording means is referred to as a "square-law" detector. As a consequence, the interference term, i.e., the term of the detector response which is sensitive to the relative phase of the interfering polarization components, is proportional to the cosine of .DELTA..phi., where .DELTA..phi. is the difference in the phase of the light between the polarization components emanating from a single point in the object volume.
Terms relevant to both the prior art and the current invention are defined with reference to FIG. 1 which is a simplified depiction of a prior art conoscope, designated generally by numeral 10. The axis (not shown) of anisotropic crystal 12 having the highest degree of rotational symmetry is referred to, conventionally, as the "optical axis" of the crystal, and in the simplified "on-axis" case depicted in FIG. 1, is assumed to coincide with the geometrical axis z of the system. Light emanating from point P of the source region passes through crystal 12 with the phase difference .DELTA..phi. of one polarization with respect to the other given, for light reaching detector plane 14 at point Q by: EQU .DELTA..phi.=(.pi..kappa..sub.O) r.sup.2 /z.sub.c.sup.2,
where:
r is the lateral displacement in detector plane 14 of point Q from the geometrical axis z whose intersection with detector plane 14 is designated Q'; PA1 .kappa..sub.O is the unitless conoscopic parameter defined in equation A-13 of Sirat; and PA1 z.sub.c is the conoscopic corrected distance, defined in equation A-8 of Sirat, which can be converted to the actual distance between conoscope 10 and object point P by knowledge of system parameters, as taught by Sirat, or by calibration means known in the art.
Additionally, if the optic axis of crystal 12 is displaced with respect to the geometrical axis of the system by an angle, referred to as the "off-axis angle," .theta..sub.OFF, taken, without loss of generality, to be in the direction of the x axis, then the phase difference .DELTA..phi. is given by: EQU .DELTA..phi.=(.pi..kappa..sub.O) ((x-x.sub.O -.theta..sub.OFF z.sub.c).sup.2 +(y-y.sub.O).sup.2)/z.sub.c.sup.2,
where x.sub.O and y.sub.O refer to the coordinates of the geometric axis in detector plane 14.
In either the on-axis or more general case, it can be seen that the phase difference .DELTA..phi. depends quadratically on the displacement of detector point Q from the geometric axis, and, more particularly, depends quadratically on the displacement of detector point Q from the geometric axis along a particular direction in the detector plane. This behavior is referred to as a "quadratic fringe," and is illustrated by the inteferogram shown in FIG. 2. The resulting pattern of annular interference fringes is referred to as a Gabor Lens Zone interferogram.
In practical applications of conoscopy, which include quality inspection in the production of precision components, speed and precision requirements suggest the advantages of replacing the known quadratic, or parabolic, dependence of the interference pattern on distance from the center of the GZL with a linear fringe fundamental response. In the prior art quadratic case, determination of the distance to the object point requires simultaneous determination of two parameters: the centroid and coefficient of the parabola. The measurement is correspondingly less accurate, for a given exposure, than in the linear case, where the same measurement requires algorithmic determination of the slope alone. Additionally, deconvolution of the interferogram in the known quadratic case requires specialized, and necessarily more complex and time-consuming, computational algorithms. Additionally, the quadratic dependence introduces an aberration due to the orientation of the extraordinary axis of the birefringent medium in each of the two orthogonal planes containing the optical axis of the system. This phenomenon effectively reduces the useful numerical aperture of the system, and, consequently, limits the light flux which can be captured in the detector plane, and increases the time required for a specified level of measurement accuracy.